On the Spurious Mode Generation Induced by Spectral-Like Optimized Interpolation Schemes Used in Computational Acoustics (Communications in Computational Physics, 2018)
The present work constitutes a fraction of a more extensive study that isdevoted to numerical methods in acoustics. More precisely, we address here the interpolationprocess, which is more and more frequently used in Computational Acoustics– whether it is for enabling multi-stage hybrid calculations, or for easing the properhandling of complex configurations via advanced techniques such as Chimera grids orImmersed Boundary Conditions. In that regard, we focus on high-order interpolationschemes, so as to analyze their intrinsic features and to assess their effective accuracy.Taking advantage of specific insights that had been previously achieved by the presentauthors regarding standard high-order interpolation schemes (of centered nature), wehere focus on their so-called spectral-like optimized counterparts (of both centered andnoncentered nature). The latter spectral-like optimized schemes are analyzed thoroughlythanks to dedicated theoretical developments, which allow highlighting betterwhat their strengths and weaknesses are. Among others, the various ways such interpolationschemes can degrade acoustic signals they are applied to are carefully investigatedfrom a theoretical point-of-view. Besides that, specific criteria that could help inoptimizing interpolation schemes better are provided, along with generic rules abouthow to minimize the signal degradation induced by existing interpolation schemes, inpractice.